The majority of natural scenes contains zones that are visible to one eye only. Past studies have shown that these monocular regions can be seen at a precise depth even though there are no binocular disparities that uniquely constrain its location in depth. In the so-called da Vinci stereopsis configuration, the monocular region is a vertical line placed next to a binocular rectangular occluder. The opacity of the occluder has been mentioned to be a necessary condition to obtain da Vinci stereopsis. However, this opacity constraint has never been empirically tested. In a first experiment, we tested whether there exists an interaction between classical stereopsis and perceptual transparency. Observers had to judge the depth ordering of two overlapping rectangles. The probability of seeing one surface in front of the other varied with the relative transmittance of the two rectangles. For each trial, a given disparity was added to one of the two surfaces, favoring one of the two to be seen in front. These two depth cues were varied independently. We found a significant interaction between the transmittance and the relative disparity of the rectangles suggesting that these two depth cues can be combined efficiently by the visual system. In the second experiment, we tested whether da Vinci stereopsis and perceptual transparency can interact using a classical da Vinci configuration in which the transparency of the occluder varied. We found that the monocular line was perceived according to the geometry of occlusion present in the scene even when the occluder was clearly transparent. Taken together, these results indicate that the mechanism responsible to place monocular regions in depth is not sensitive to the material properties of objects and da Vinci stereopsis is solved during the early stages of disparity processing.